It is well known that the active set algorithm is very effective for smooth box constrained optimization. Many achievements have been obtained in this field. We extend the active set method to nonsmooth box constrained optimization problems, using the Moreau-Yosida regularization technique to make the objective function smooth. A limited memory BFGS method is introduced to decrease the workload...

This paper proposes a competitive divide-and-conquer algorithm for solving large-scale black-box optimization problems, where there are thousands of decision variables, and the algebraic models of the problems are unavailable. We focus on problems that are partially additively separable, since this type of problem can be further decomposed into a number of smaller independent sub-problems. The ...

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic – based on the CGRASP and GENCAN methods – for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN on a set of bench...

Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. In the robust optimization framework the problem solved is a min-max problem where a solution is judged according to its performance on the worst possible realization of the parameters. In many cas...

The ideas of robust sets, robust functions and robustness of general set-valued maps were introduced by Chew and Zheng [7, 26], and further developed by Shi, Zheng, Zhuang [18, 19, 20], Phú, Hoffmann and Hichert [8, 9, 10, 17] to weaken up the semi-continuity requirements of certain global optimization algorithms. The robust analysis, along with the measure theory, has well served as the basis ...

This paper addresses a robust multi-objective optimization approaches for tuning Generator Excitation PSS system parameters of power systems. The objective function which is a composite of different performance indices corresponding to different disturbances and steady-state operating conditions is then posed as a multi-objective nonlinear optimization problem together with parameters from a gi...

Heuristic optimization provides a robust and efficient approach for extracting approximate solutions of multi-objective problems because of their capability to evolve a set of non-dominated solutions distributed along the Pareto frontier. The convergence rate and suitable diversity of solutions are of great importance for multi-objective evolutionary algorithms. The focu...

We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explicit optimization problems. Moreover, we develop simplified reformulations for problems with uncertainty sets ...